The grades on a math midterm at Loyola are normally distributed with $\mu = 81$ and $\sigma = 2.5$. Tiffany earned a n $82$ on the exam. Find the z-score for Tiffany's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Tiffany's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{82 - {81}}{{2.5}}} $ ${ z \approx 0.40}$ The z-score is $0.40$. In other words, Tiffany's score was $0.40$ standard deviations above the mean.